We study the following two nonlinear evolution equations with a fourth order (biharmonic) leading term: (Formula presented.) and (Formula presented.) with an initial value and a Dirichlet boundary conditions. We show the existence and uniqueness of the weak solutions of these two equations. For any t ∈ [0, + ∞), we prove that both solutions are in (Formula presented.). We also discuss the asymptotic behavior of the solutions as time goes to infinity. This work lays the ground for our numerical simulations for the above systems [M.J. Lai, C. Liu and P. Wenston (2004). Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations. Applicable Analysis, 83, 563–577].
All Science Journal Classification (ASJC) codes
- Environmental Chemistry
- Plant Science